Explanation of the Meyer-Neldel Rule
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1 Explanation of the Meyer-Neldel Rule P. Stallinga, Universidade do Algarve (FCT, OptoEl, CEOT) Rudolstadt, 30 September 2004
2 Trap states as an explanation of the Meyer-Neldel Rule P. Stallinga, Universidade do Algarve (FCT, OptoEl, CEOT) Rudolstadt, 30 September 2004
3 Overview What is the Meyer-Neldel Rule? Background: Traps in organic FETs in Faro Results and discussion
4 OptoEl-CEOT in Faro Specialized in electronic characterization of organic and biological electronic devices. Sensitive equipment with custom made control software. DLTS (the only organic DLTS) Organics-specific FET measurement system
5 What is the Meyer-Neldel Rule? Observation without explanation* The thermal activation energy of a process (P) depends on a certain parameter (z). There exists a temperature (T MN ) where the dependence of P on z disappears. P = P 0 exp( E A /kt) P 0 = P MN exp(e A /kt MN ) * Original article: W. Meyer and H. Neldel, Z. Techn. 18, 588 (1937).
6 Examples of the Meyer-Neldel Rule Processes current diffusion* ionic currents Parameters gas concentration pressure electrical bias Devices/materials α-si organic ½cons gas detectors High-Tc supercons glasses liquid ½cons polycryst. Si CCDs * Here the MNR is called the Compensation Effect.
7 Examples of the Meyer-Neldel Rule Processes current diffusion* ionic currents Parameter gas concentration pressure electrical bias Devices/materials α-si organic ½cons gas detectors High-Tc supercons glasses liquid ½cons polycryst. Si CCDs All less-than-perfect-crystalline materials * Here the MNR is called the Compensation Effect.
8 Meyer-Neldel Rule in our T6 TFT Phase transition (?) at 200 K P. Stallinga et al., J. Appl. Phys. October 2004
9 Non-linear transfer curves Start with classic theory. However: Non-linear Transfer curves observed
10 Non-linear transfer curves Currents are linearized by taking the n th root Recently explained on model for amorphous silicon, see P. Stallinga, J.Appl.Phys. October Traps!
11 Poole-Frenkel Non-linear IV curves observed
12 Poole-Frenkel Non-linear IV curves explained The fact that the plot is linear in this scale proofs the validity of the model of Poole- Frenkel. P. Stallinga, J.Appl.Phys. October Traps!
13 Stressing H.L. Gomes, Appl.Phys.Lett Note: Already the fact that a threshold voltage exists in an accumulation-type FET proofs the existence of traps! Theoretically, the threshold voltage is zero (or >0, Normally-on FET ). Traps!
14 Decaying currents
15 Decaying currents I(t) = I 0 exp(-(t/τ) α ) 4 th root of Time (s) Glassy relaxation * or stretched exponential. Transient caused by trapping. P. Stallinga, J.Appl.Phys. October *original article: R. Kohlrausch in Rinteln, Ann. Phys. und Chemie 72, 353 (1847). Traps!
16 Thermally scanned current E A = 170 mev h E C E T E V Tr Tr + h or Tr + Tr + h An I-T curve shows that charges are liberated from trap states. I(T) µx p(t) not: I(T) µ(t) x p Traps!
17 Charges are liberated from trap states. not I(T, V g ) µ(t, V g ) x p but I(T, V g ) µx p(t, V g )
18 Amorphous silicon: Shur & Hack * Original article: M. Shur and M. Hack, J. Appl. Phys. 55, 3831 (1984).
19 Shur & Hack (53) (51) Notes: A factor q was deleted from original Equation 51. The model is similar to Vissenberg s, with difference that conduction is through band states instead of hopping conduction.
20 Linking Shur-Hack to our organic FETs I ds depends on V g, but not in a classical way (not V g ). Non-linear transfer curves (53) (51)
21 Linking Shur-Hack to Meyer-Neldel First halve of Meyer-Neldel Rule: Dependence on V g disappears at a temperature T = 2T 2. (53) (51)
22 Linking Shur-Hack to Meyer-Neldel Second halve of Meyer-Neldel Rule: Activation energy depends on V g : For T << T 2 the Arrhenius plots are linear and (53) (51) Used: sin(x) x for x << 1 and a x = exp(x ln(a))
23 Simulation Note: No measurements possible at/close to T 2 (currents drop and diverge).
24 Experiment. Sexithiophene TFT V ds = 0.5 V V g = 10.5 V 35F_Ux.m Note: To avoid stressing, measurements limited to below 220 K (see talk of Henrique)
25 Experiment. Sexithiophene TFT fitting 35F_Ux.m
26 Conclusions 3 things important for organic FETs (T6): Traps traps & traps A: Responsible for non-linear transfer curves (I ds V gγ ) A: Responsible for non-linear IV curves (I ds V ds exp(- V ds ) ) A: Responsible for temperature activation of current A: (P. Stallinga et al., J. Appl. Phys., Oct. 2004) B: Responsible for stressing B: (H.L.Gomes et al., Appl. Phys. Lett. 2004) C: Responsible for the Meyer Neldel Observation C: (P. Stallinga et al., to be published) Thanks: Henrique Gomes (OptoEl/CEOT) All members of the MONA-LISA network CNR-ISM Bologna
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